In concentrating pulps from concentrations of from 1-5% up to 8-15% or higher, the necessary amount of liquid to be removed can be separated by a screening device without the need to supply any replacing liquid. When washing or treating with chemicals, such as in bleaching, the treatment liquid is supplied through a special device, which is arranged with respect to the screening device so that the liquid so supplied is passed through the suspension transversely to the direction of flow of the suspension. Such a transverse flow has the effect that the liquid in which the fiber material is suspended is entirely or partially exchanged against the liquid so supplied.
While the fibrous suspension is being passed through a passageway, the liquid can be screened off through a screening device, thus resulting in a pulp body with an increased fiber concentration. This, however, can give rise to plug formation in the passageway and thereby render continued screening impossible. This problem has been eliminated by the method and apparatus of the present invention.